# Implicit Posterior Variational Inference for Deep Gaussian Processes

arXiv: https://arxiv.org/abs/1910.11998 · HTML: https://mlsanity.com/paper/1910.11998/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2019.

## Built on by (most cited first, 17 of 17)

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- [Conditional Deep Gaussian Processes: empirical Bayes hyperdata learning](https://mlsanity.com/paper/2110.00568/) (2021)
- [On Connecting Deep Trigonometric Networks with Deep Gaussian Processes: Covariance, Expressivity, and Neural Tangent Kernel](https://mlsanity.com/paper/2203.07411/) (2022)
- [Deep Latent Force Models: ODE-based Process Convolutions for Bayesian Deep Learning](https://mlsanity.com/paper/2311.14828/) (2023)
- [Onsager-Machlup Posterior Transport for Deep Gaussian Processes](https://mlsanity.com/paper/2605.23434/) (2026)
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## Abstract (arXiv)

A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic approximation methods. Unfortunately, the deterministic approximation methods yield a biased posterior belief while the stochastic one is computationally costly. This paper presents an implicit posterior variational inference (IPVI) framework for DGPs that can ideally recover an unbiased posterior belief and still preserve time efficiency. Inspired by generative adversarial networks, our IPVI framework achieves this by casting the DGP inference problem as a two-player game in which a Nash equilibrium, interestingly, coincides with an unbiased posterior belief. This consequently inspires us to devise a best-response dynamics algorithm to search for a Nash equilibrium (i.e., an unbiased posterior belief). Empirical evaluation shows that IPVI outperforms the state-of-the-art approximation methods for DGPs.